Question

write an explicit formula for $a_n$, the $n^{\text{th}}$ term of the sequence 4, 12, 36,.... answer attempt 1 out of 2

Explanation:

Step1: Identify the sequence type

Check if it's geometric. Divide second term by first: $\frac{12}{4} = 3$. Third term by second: $\frac{36}{12} = 3$. So common ratio $r = 3$.

Step2: Recall geometric sequence formula

The explicit formula for a geometric sequence is $a_n = a_1 \cdot r^{n - 1}$, where $a_1$ is the first term and $r$ is the common ratio.

Step3: Substitute values

Here, $a_1 = 4$ and $r = 3$. So $a_n = 4 \cdot 3^{n - 1}$.

Answer:

$a_n = 4 \cdot 3^{n - 1}$